Approximation (A-C)/(B-D) ~= A/B + ...?

In the data reduction of a physics experiment i am conducting, it could be advantageous

to input A/B as a parameter instead of A and B separately.

The data reduction program now has this form:

output = (A-C)/(B-D)

with A,B,C,D physical input parameters (some measured, some material constants).

My question: how can I find an approximation that has A/B as the first term:

output = A/B + f(A/B,C,D)

with f(A/B,C,D) a function of the ratio A/B, and the remaining parameters C and D.

This data reduction program only uses A/B as a parameter.

The name of a systematic approach or anything related are very welcome,

thank you for your time.